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Entangling gates in trapped-ion quantum computing have primarily targetedstationary ions with initial motional distributions that are thermal and closeto the ground state. However, future systems will likely incur significantnon-thermal excitation due to, e.g., ion transport, longer operational times,and increased spatial extent of the trap array. In this paper, we analyze theimpact of such coherent motional excitation on entangling-gate error byperforming simulations of Molmer-Sorenson (MS) gates on a pair of trapped-ionqubits with both thermal and coherent excitation present in a shared motionalmode at the start of the gate. We discover that a small amount of coherentdisplacement dramatically erodes gate performance in the presence ofexperimental noise, and we demonstrate that applying only limited control overthe phase of the displacement can suppress this error. We then use experimentaldata from transported ions to analyze the impact of coherent displacement onMS-gate error under realistic conditions.

Entangling-gate error from coherently displaced motional modes of trapped ions